Complexity of Bezout ’ S Theorem Iv : Probability of Success ; Extensions

  title={Complexity of Bezout ’ S Theorem Iv : Probability of Success ; Extensions},
  author={Michael Shub and Steve Smale},
Michael Shub and Steve Smale Abstra t. We estimate the probability that a given number of projective Newton steps applied to a linear homotopy of a system of n homogeneous polynomial equations in n + 1 complex variables of fixed degrees will find all the roots of the system. We also extend the framework of our analysis to cover the classical implicit function theorem and revisit the condition number in this context. Further complexity theory is developed. 
Highly Influential
This paper has highly influenced 16 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS

From This Paper

Figures, tables, results, connections, and topics extracted from this paper.
90 Extracted Citations
21 Extracted References
Similar Papers

Citing Papers

Publications influenced by this paper.
Showing 1-10 of 90 extracted citations

Referenced Papers

Publications referenced by this paper.
Showing 1-10 of 21 references

Some remarks on Bezout’s Theorem and complexity theory, to appear in “From Topology

  • M. Shub
  • 1987
Highly Influential
7 Excerpts

Newton’s Method estimates from data at one point, in “The Merging of Disciplines

  • S. Smale
  • 1981
Highly Influential
3 Excerpts

Complexity of Bezout ’ s Theorem I : Geometric aspects ( referred to as Bez I )

  • M. Shub, S. Smale
  • J . of the Amer . Math . Soc .
  • 1993

Complexity of Bezout’s Theorem II: Volumes and probabilities

  • M. Shub, S. Smale
  • of the Amer. Math. Soc
  • 1993

Invariant Manifolds, Springer Lecture Notes # 583

  • M. Hirsch, C. Pugh, M. Shub
  • 1992

Sphere Packings, Lattices and Groups, Springer, New York, 1988. Demmel, J., On condition numbers and the distance to the nearest ill-posed problem, Numerische Math

  • J. 1–46. Conway, N. Sloane
  • 1988

On condition numbers and the distance to the nearest illposed problem

  • J. Demmel
  • Numerische Math .
  • 1987

Similar Papers

Loading similar papers…